One of the many hypotheses on the pathogenesis of Alzheimer's disease is that the amyloid-beta peptide (Abeta) binds CuII and can catalytically generate H2O2, leading to oxidative damage in brain tissues. For a molecular level understanding of such catalysis it is critical to know the structure of the Abeta-CuII complex precisely. Unfortunately, no high-resolution structure is available to date and there is considerable debate over the copper coordination environment with no clear consensus on which residues are directly bound to CuII. Considering all plausible isomers of the copper-bound Abeta42 and Abeta40 using a combination of density functional theory and classical molecular dynamics methods, we report an atomic resolution structure for each possible complex. We evaluated the relative energies of these isomeric structures and surprisingly found that Abeta42 and Abeta40 display very different binding modes, suggesting that shorter peptides that are truncated at the C-terminus may not be realistic models for understanding the chemistry of the most neurotoxic peptide, Abeta42.